Can I combine two classifiers that make different kinds of errors to get a better classifier?
Yes, you can. There are a lot of different techniques, usually called Ensemble Methods. 

A better approach might be to use something like AdaBoost along with a cheaper method like the decision trees you looked at. AdaBoost explicitly tries to train classifiers to correctly handle different parts of the data, rather than hoping that different methods turn out to do so by chance.